Answer
There are 10 core electrons and 4 valence electrons and 2 unpaired electrons.
Work Step by Step
Silicon has 14 electrons. The electron configuration of silicon is $$Si: 1s^22s^22p^63s^23p^2$$
The nearest noble gas element of lower atomic number is $Ne$, which has the electron configuration $1s^22s^22p^6$. Therefore, the condensed electron configuration of nitrogen is $$Si: [Ne]3s^23p^2$$
1) Looking here, we see that there are 10 inner-shell electrons (those that occupy the first and second shells) and 4 outer-shell electrons (those that occupy the third shell). Also, since silicon has the atomic number less than 30, all outer-shell electrons are valence electrons.
Therefore, there are 10 core electrons and 4 valence electrons.
2) The unpaired electrons are those who does not have the accompanying electrons which have the opposite electron spin in an orbital.
We see from the electron configuration of silicon that the first and second shells and the s-subshell of the third shell have been fully occupied.
Therefore, let's look at the p subshell of the third shell.
The maximum number of electrons that a p subshell can have are 6 (p subshell has 3 orbitals, each orbital can carry 2 electrons at most). Here, only 2 electrons are present. According to Hund's rule, to achieve the most stable situation, each of these 2 electrons will occupy a separate orbital that a p subshell has.
That means only 2 orbitals here carries 1 electron each, 1 orbital does not contain any electrons. Therefore, there are 2 unpaired electrons in silicon.